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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 214 · 40 questions
TalentJR

How to solve it (Across, up, Pythagoras): Distance: across = difference of the x values, up = difference of the y values; distance = √(across² + up²). Midpoint = ((x₁ + x₂) ÷ 2, (y₁ + y₂) ÷ 2). Quadrants by signs: (+, +) first, (−, +) second, (−, −) third, (+, −) fourth.

NameDateTime takenScore ___ / 40
  1. 1.In which quadrant does the point (5, 2) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  2. 2.What is the midpoint of the line joining (9, 12) and (17, 0)? (a) (13, 6) (b) (26, 12) (c) (6, 13) (d) (4, 6)
  3. 3.What is the midpoint of the line joining (7, 2) and (9, 8)? (a) (5, 8) (b) (1, 3) (c) (8, 5) (d) (16, 10)
  4. 4.What is the distance between the points (0, 9) and (12, 25)? (a) 400 (b) 20 (c) 21 (d) 28
  5. 5.In which quadrant does the point (5, −3) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  6. 6.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 10 (c) 100 (d) 14
  7. 7.In which quadrant does the point (6, 2) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  8. 8.What is the distance between the points (4, 15) and (13, 3)? (a) 21 (b) 15 (c) 225 (d) 16
  9. 9.What is the distance between the points (5, 5) and (14, 17)? (a) 225 (b) 21 (c) 16 (d) 15
  10. 10.What is the distance between the points (2, 7) and (9, 31)? (a) 625 (b) 25 (c) 26 (d) 31
  11. 11.How far is the point (24, 7) from the origin (0, 0)? (a) 31 (b) 625 (c) 25 (d) 26
  12. 12.What is the midpoint of the line joining (3, 13) and (7, 9)? (a) (2, 2) (b) (5, 11) (c) (11, 5) (d) (10, 22)
  13. 13.What is the midpoint of the line joining (6, 16) and (10, 4)? (a) (8, 10) (b) (2, 6) (c) (10, 8) (d) (16, 20)
  14. 14.In which quadrant does the point (9, 3) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  15. 15.What is the distance between the points (9, 1) and (24, 9)? (a) 18 (b) 17 (c) 289 (d) 23
  16. 16.In which quadrant does the point (6, −8) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  17. 17.How far is the point (16, 12) from the origin (0, 0)? (a) 20 (b) 28 (c) 400 (d) 21
  18. 18.What is the distance between the points (4, 13) and (28, 6)? (a) 31 (b) 625 (c) 25 (d) 26
  19. 19.What is the distance between the points (4, 10) and (16, 5)? (a) 17 (b) 14 (c) 13 (d) 169
  20. 20.What is the midpoint of the line joining (1, 7) and (13, 15)? (a) (11, 7) (b) (6, 4) (c) (14, 22) (d) (7, 11)
  21. 21.What is the distance between the points (9, 15) and (33, 8)? (a) 31 (b) 625 (c) 26 (d) 25
  22. 22.What is the distance between the points (9, 3) and (13, 6)? (a) 25 (b) 7 (c) 5 (d) 6
  23. 23.What is the distance between the points (3, 5) and (27, 12)? (a) 25 (b) 31 (c) 625 (d) 26
  24. 24.In which quadrant does the point (−9, 6) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  25. 25.What is the distance between the points (3, 12) and (8, 0)? (a) 169 (b) 17 (c) 14 (d) 13
  26. 26.What is the distance between the points (2, 4) and (10, 10)? (a) 14 (b) 100 (c) 11 (d) 10
  27. 27.In which quadrant does the point (−8, 1) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  28. 28.In which quadrant does the point (1, 2) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  29. 29.What is the distance between the points (6, 19) and (15, 7)? (a) 16 (b) 21 (c) 225 (d) 15
  30. 30.What is the distance between the points (0, 11) and (8, 5)? (a) 14 (b) 100 (c) 11 (d) 10
  31. 31.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 17 (c) 169 (d) 13
  32. 32.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 23 (c) 289 (d) 17
  33. 33.What is the midpoint of the line joining (0, 6) and (4, 16)? (a) (4, 22) (b) (11, 2) (c) (2, 11) (d) (2, 5)
  34. 34.What is the distance between the points (7, 2) and (16, 14)? (a) 21 (b) 15 (c) 16 (d) 225
  35. 35.What is the distance between the points (8, 1) and (16, 16)? (a) 23 (b) 17 (c) 18 (d) 289
  36. 36.In which quadrant does the point (5, −9) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  37. 37.What is the distance between the points (8, 7) and (17, 19)? (a) 16 (b) 225 (c) 21 (d) 15
  38. 38.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 26 (c) 25 (d) 31
  39. 39.In which quadrant does the point (−4, 3) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  40. 40.In which quadrant does the point (7, 9) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant

Answer key

  1. First quadrant
  2. (13, 6)
  3. (8, 5)
  4. 20
  5. Fourth quadrant
  6. 10
  7. First quadrant
  8. 15
  9. 15
  10. 25
  11. 25
  12. (5, 11)
  13. (8, 10)
  14. First quadrant
  15. 17
  16. Fourth quadrant
  17. 20
  18. 25
  19. 13
  20. (7, 11)
  21. 25
  22. 5
  23. 25
  24. Second quadrant
  25. 13
  26. 10
  27. Second quadrant
  28. First quadrant
  29. 15
  30. 10
  31. 13
  32. 17
  33. (2, 11)
  34. 15
  35. 17
  36. Fourth quadrant
  37. 15
  38. 25
  39. Second quadrant
  40. First quadrant

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